Geometry of discrete copulas
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1802.06969.pdf
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Author(s)
Perrone, Elisa
Solus, Liam
Uhler, Caroline
Uhler, Caroline
Date Issued
July 2019
Journal
Journal of Multivariate Analysis
Publisher
Elsevier BV
Citation
Perrone, Elisa et al. "Geometry of discrete copulas." Journal of Multivariate Analysis 172 (July 2019): 162-179 © 2019 Elsevier
Version
Author's final manuscript
Abstract
The space of discrete copulas admits a representation as a convex polytope, and this has been exploited in entropy-copula methods used in hydrology and climatology. In this paper, we focus on the class of component-wise convex copulas, i.e., ultramodular copulas, which describe the joint behavior of stochastically decreasing random vectors. We show that the family of ultramodular discrete copulas and its generalization to component-wise convex discrete quasi-copulas also admit representations as polytopes. In doing so, we draw connections to the Birkhoff polytope, the alternating sign matrix polytope, and their generalizations, thereby unifying and extending results on these polytopes from both the statistics and the discrete geometry literature.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jmva.2019.01.014
